All three examples sound correct to me. You could even say
Du siehst heute wie ein Mädchen aus.
However you would usually try to keep the connection as close as possible. So the first and second example are "better" than the third or mine above.
It might get hard to get the context if the sentence gets longer. For example:
Ich füllte das Formular ...

Yes, both sources are correct. The regular comparative is formed with the ending -er, so "neuer" is the comparative of "neu":
neu, neuer, am neuesten
Then we have the endings in the declension of adjectives, and yes, for the indefinite article, the nominative ending is also -er:
ein neuer Wagen
Yes, it sounds confusing, but we all will just have ...

There are subtle differences when using a superlative for an idiomatic group or when using it simply with plural. This can nicely be shown with the examples you gave.
Superlative and plural
It was the darkest of nights. - Es war die dunkelste aller Nächte.
Note that we can use "aller" here to put emphasis on the fact that a variable number of many ...

The correct translation would be
Netflix ist besser als DVDs zu kaufen oder ins Kino zu gehen.
While in English you use a gerund when comparing things, in German you use the preposition "zu" with the verb, literally translated as
Netflix is better than to buy DVDs or to go to the cinema.
In informal use, you could even leave out the "zu", as ...

mein is one of the german possessive pronouns mein (ich), dein (du), sein (er), ihr (sie), sein (es), unser (wir), euer (ihr), ihr (sie), Ihr (Sie) (the words in brackets are the corresponding german personal pronouns). They (the possessive pronouns) can be inflected to act as possessive articles:
Mein Deutsch ist besser.
But they can be also used ...

Wegfahren (drive off) is focussing on a short movement from a given location without concern for a final destination, although this movement might as well be only the beginning of a longer journey. The means of transport is usually a private one, a car, motorcycle, bicycle, etc.:
Fahr von dort weg, du stehst im Halteverbot.
Ich fahre noch kurz ...

Yes, they can mean both. Now how to distinguish between them.
If an adjective stands in front of a noun it will get some sort of ending depending on case, preceding article and numerous. One possible ending is -er. The minimum ending is -e. There will never be no ending. So if you see "neuer" in front of a noun, the -er MUST be an ending and the word is ...

In a written text (which it quite likely is, because "auf dem Lande" would be used only by exclusively educated people with very refined, not to say Mannerist speaking habits), "Ich bin jetzt nicht so glücklich wie früher auf dem Lande" leaves open the question A) whether you were happy when you used to be in the country as opposed to now being somewhere ...

preface
The sentence is completely fine as it is. It is ambiguous as described in the comments and the other answer. But people speak like that (well, except they don't say "Lande") and they understand each other. There is no need to rephrase it; it is fit for print. Also, the possible double meaning has no bearing on the question itself and is henceforth ...

I can only speculate about the origin of this grammatical feature but als dass is used if the als is comparitive (than) while only als is used if the als is temporal (when).
Some examples:
Er stand lieber früh auf, als dass er arbeitslos war.
He rather got up early than being unemployed (e.g., because he got a job that required him getting up early).
...

Suppose the given sentence is slightly different.
Skype ist besser als Leute zu treffen oder anzurufen.
Then it would be natural, altough perhaps not necessary, to convert both things you are comparing to the same kind of grammatical object, i.e. to verbalize the left hand side or to nominalize the right hand side:
Verbalization.
Skypen ist ...